Is it farther or further?
late 14c., durand, present participle of obsolete verb duren "to last, endure" (mid-13c.), from Old French durer, from Latin durare "endure" (see endure). During the day really is "while the day endures," and the usage is a transference into English of a Latin ablative absolute (cf. durante bello "during (literally 'enduring') the war").